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We present, as a very general method, an effective field theory to analyzemodels defined over small-world networks. Even if the exactness of the methodis limited to the paramagnetic regions and to some special limits, it gives theexact critical behavior and the exact critical surfaces and percolationthresholds, and provide a clear and immediate (also in terms of calculation)insight of the physics. The underlying structure of the non random part of themodel, i.e., the set of spins staying in a given lattice L_0 of dimension d_0and interacting through a fixed coupling J_0, is exactly taken into account.When J_0\geq 0, the small-world effect gives rise to the known fact that asecond order phase transition takes place, independently of the dimension d_0and of the added random connectivity c. However, when J_0<0, a completelydifferent scenario emerges where, besides a spin glass transition, multiplefirst- and second-order phase transitions may take place.

Exact results and new insights for models defined over small-world networks. First and second order phase transitions. I: General result